HI! Is toothpaste is good medicine for hot oil burn on hand during cooking?

Not recommended. As toothpastes contain harmful chemicals like calcium and peppermint it increases the risk of skin infection. The first aid for a burn is immediate application of cold water or ice.
Absolutely not. The toothpaste will only irritate your burn even more. If the burn is bad, you should see a physician for proper care.
NO! Toothpaste is formulated to be used in the mouth, nowhere else. It can irritate skin and make a burn worse. First aid for a burn is ice. If burn is serious or distributed over a wide area see your GP or Urgent Care for burn treatment. But do not use toothpaste.